Sea surface height (SSH) changes result from changes in steric height (SH) and mass. We investigate total SH and mass from co-located measurements of SSH and SH in the upper 1500 dbar (SH0–1500). SSH changes are decomposed into SH0–1500 and ‘other’ contributions, where ‘other’ includes SH changes below 1500 dbar and mass changes. This is done using satellite altimeter measurements of SSH available since late 1992 in combination with WOCE-era hydrography and Argo. A hemispheric analysis of co-located WOCE and Argo profiles gives robust ΔSH/ΔSSH relationships, varying with latitude. The ΔSH/ΔSSH ratio together with satellite SSH yields an estimate of decadal SH increase. It is found that ∼0.5 of the hemispheric decadal SSH rise is steric, with this proportion increasing southwards. The relatively large rate of SSH increase south of 30°S, the high proportion attributable to SH (i.e., ocean warming) and the great area of the southern ocean, mean the total heat gain south of 20°S is comparable to estimates of global 0-700 m heat gain for this period.
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 Since the early 1990s global mean SSH and ocean heat content (OHC) have risen at substantial rates at least as large as their 50-year trends. Since 1993, SSH has increased by 3 mm/yr [Merrifield et al., 2009], compared to 1.8 mm/yr for the long-term trend [Church et al., 2004], while 0–700 m OHC has increased by ∼1.0 × 1022 J/year [Lyman et al., 2010], greater than the multi-decadal 0.3 × 1022 J/year [Levitus et al., 2009].
 The increases in SSH and possibly OHC since the early 1990s have occurred disproportionately in the southern hemisphere [Merrifield et al., 2009]. The causes of large southern signals in the work of Willis et al.  and Lombard et al.  are uncertain, as are the spatial patterns of associated steric and mass contributions. Southern warming has been attributed to increases in the wind-driven subtropical gyre [Roemmich et al., 2007] and/or a southward shift in the Antarctic Circumpolar Current [Gille, 2008].
 The ocean observing system has undergone major evolution in recent decades. The early 1990s saw the instigation of high-accuracy satellite altimetry and the World Ocean Circulation Experiment (WOCE) global hydrographic survey. More recently, the Argo profiling float array has been implemented and now obtains CTD profiles in the upper 2000 m with broad-scale global coverage.
 The satellite altimeter and WOCE-to-Argo era of modern global hydrography have yielded improved estimates of SSH and OHC. Remaining challenges for the observing system are that shipboard deep hydrography lacks the spatial coverage needed to adequately resolve the pattern of global change and Argo stops short of the abyssal ocean where warming is a significant contribution to SH [Purkey and Johnson, 2010].
 This work studies the relationship between changes in SSH and SH0–1500 on decadal time-scales. It uses this relationship to inform the unknown deeper SH and mass variations that complete the SSH budget. With global coverage of SSH throughout the study period and of SH0–1500 by Argo in the present era, the limiting spatial factor is the WOCE-era hydrography. A goal is to extract the information content of the integrated ocean observing system, and to understand limitations in order to chart future improvement. Plans call for Argo to extend into the deep ocean [Freeland et al., 2010]. This will be a difficult technical challenge, and it is important to learn as much as possible about the requirements and the benefits of a deep-ocean float array.
2. Co-located WOCE-Era and Argo Data
 The initial hydrographic conditions are from ship-based data primarily obtained as part of WOCE. A total of 3456 CTD and hydrocasts were extracted from the World Ocean Database [e.g., Locarnini et al., 2010] for the region between 20°S and 62°S, the period 1 Oct 1992 to 31 Dec 1997 (the earliest five year interval coinciding with satellite altimeter data), and extending to at least 1500 m.
 The final hydrographic conditions are defined by Argo data collected between 2004 and 2008. Only data subjected to Argo's delayed-mode quality control process were used [e.g., Owens and Wong, 2009]: these have been corrected for salinity drift, pressure drift, and other problems. Argo profiles were considered to be co-located with a WOCE-era profile if they were within 0.5° in lat and lon, resulting in 26925 Argo/WOCE-era pairs corresponding to 2917 WOCE-era profiles. SH0–1500 was calculated for both the WOCE-era and Argo profile data.
 SSH based on satellite altimetry came from the AVISO “reference” product [Ducet et al., 2000], with grid spacing of 1/3° lat × 1/3° lon × 1 week. Nearest grid point SSH values were extracted for the initial and final member of every profile pair. This provided a difference in SSH corresponding to each difference in SH0–1500.
 This analysis is focused on decadal variability, but the co-located differences contain noise including seasonal variations, mesoscale eddies, and differences due to spatial offsets of the profile pairs. The seasonal variations in SH0–1500 and SSH were removed from the initial and final values using a seasonal cycle from a gridded Argo dataset [Roemmich and Gilson, 2009] and the gridded SSH product, respectively.
 Mesoscale variability is evident in the WOCE transects, which have typical along-track resolution of about 0.5°. On average there are ∼9 Argo matchups with each WOCE-era profile and therefore the noise in the Argo endpoint is reduced by averaging. However, the sparse sampling of the WOCE era cannot be entirely overcome.
3. Decadal Changes in SSH and SH
 The seasonal cycle was removed and SH0–1500 and SSH differences were calculated between each Argo/WOCE-era pair. These differences were then normalised by the temporal separation between the samplings to give units of cm/decade. Finally, all of the Argo/WOCE-era differences for each location were averaged to give a single mean rate of change of ΔSH0–1500 (Figure 1a) and ΔSSH for each WOCE-era location.
Figures 1b and 1c show the zonally-averaged (over co-located pairs) ΔSH0–1500 (b) and ΔSSH (c) along with standard errors. In the calculation of standard error, a constant degrees of freedom (N) of 20 was used, chosen to conservatively represent the number of independent north–south WOCE survey lines. Figure 1a indicates the large gaps between WOCE transects, and raises the question of undersampling in the zonal means. Figure 1c also shows the zonally-averaged ΔSSH based on the full gridded SSH dataset, for comparison with the subsampled one: the two are quite different.
 The ΔSH0–1500 and ΔSSH values at the co-located Argo/WOCE-era locations are plotted against each other in Figure 2 for three latitude bands. It is unsurprising and clear that ΔSH0–1500 and ΔSSH are correlated, with the latter being larger in magnitude. The lines which minimise the sum of the squares of the perpendicular distances to the ΔSH0–1500/ΔSSH points are superimposed on each panel. For the entire domain, the best-fit slope was 1.38, i.e., the changes in SSH are ∼1.4 times the changes in SH0–1500. The y-intercept of the best-fit line was 2.1 cm/decade. For the three latitude bands shown in Figure 2, from south to north, the best fit slopes were 1.71, 1.37, and 1.09 respectively, and the ΔSSH/decade intercepts were 1.27, 1.62, and 2.53.
 Investigating the relationship between ΔSH0–1500 and ΔSSH further, ΔSSH can be expressed
If we assume that the deep SH change, but not the mass change, is correlated with the upper ocean SH change, i.e., ΔH1500–∞ = αΔSH0–1500 then
where the ^ denotes that the term is estimated based on the assumption. Thus, under this assumption, the slope of ΔSSH vs ΔSH0–1500 is (1+ α) and the intercept is Δass.
 This assumption fails if there are significant deep steric contributions to ΔSSH that are uncorrelated with the shallow ones, or if there are mass (barotropic) variations that are correlated to the baroclinic change. ΔH1500–∞ and Δass can be precisely described as the components of ΔSH1500–∞ and ΔMass that are correlated and uncorrelated with ΔSH0–1500 respectively. Testing this assumption could be undertaken with deep measurements – and a deep ocean component of Argo is planned – or using a dynamical model. For now, we take the assumption to be sufficiently accurate to inform this discussion. Under the assumption, on average over the entire domain ΔH1500–∞ is 0.4 times ΔSH0–1500 and the Δass component of ΔSSH is 2.1 cm/decade.
 The latitude dependence of the relationship between ΔSH0–1500 and ΔSSH apparent in Figure 2 is further explored in Figure 3. Figure 3a shows the slope (1 + α) as a function of latitude, averaged in overlapping 10° bins. The results show that south of 35°S the ocean changes deeper than 1500 m are significantly correlated with those in the upper ocean, with ΔH1500–∞ contributing about 35% to the total ΔSH. North of 33°S, ΔH1500–∞ is small. The intercept of the correlation plot (Δass) is shown as a function of latitude in Figure 3b. Spatially-varying mass anomalies correspond to changes in barotropic circulation. A 1 cm change in SSH across the Antarctic Circumpolar Current corresponds to a change in barotropic transport of 3.6 Sv, with proportionately greater transport changes at lower latitudes. Figure 3b indicates mass contributions to ΔSSH of about 1 cm/decade south of 40°S, but 2–3 cm/decade farther north. Hence, a modest eastward flow anomaly is inferred in barotropic transport in the latitude band where there is a larger westward flow anomaly in SSH. These signals are an expression of the wind-driven gyre changes described by Roemmich et al. .
 The true zonal changes can be estimated by applying the relationships from the co-located analysis to the complete gridded SSH dataset, i.e., subtracting Δass from ΔSSH leaves ΔH0–∞; scaling this by 1/(1 + α) gives ΔH0–1500. Thus, in Figure 3c, the blue area denotes ΔH0–1500, the red ΔH1500–∞ and the black Δass with all of the colored areas summing to the zonal mean ΔSSH from the gridded AVISO dataset.
 The impact of sparse sampling in the co-located pairs analysis can be estimated. Consistent with the focus on large scale decadal variability, empirical orthogonal functions (EOFs) were calculated from the AVISO SSH smoothed with a 1-year running mean and a 5° × 3° boxcar in lat and lon. Figure 4 shows the spatial pattern and time evolution of the first EOF which accounts for 56% of the variance. For comparison, the second EOF accounts for 11% of the variance and shows no trend.
 The co-located ΔSSH and ΔSH0–1500 pairs were projected onto the first EOF as follows. Let H be an N × 1 vector consisting of the height changes at co-located data points. K is an N × M matrix, with each row of K comprising zeros with the exception of a value of −ki /+ki at the indices corresponding to the initial and final sampling times. The value of ki is the amplitude of the EOF at the sample location. The matrix equation H = KA then represents the height changes, and finding the time-varying amplitude of the fit of the co-located differences to the spatial EOF amounts to solving for A, i.e., A = (KTK + ɛI)−1KTH. A small amount of noise (ɛ = 0.01) was added to condition the problem - the value of ɛ did not affect the result significantly.
 As the focus is on interannual variability, and the EOF is based on a 1-year running mean, the initial and final conditions were collapsed into a single transition allowing error bars to be calculated based on the scatter. Figure 4 shows the amplitudes of the first EOF for ΔSSH and ΔSH0–1500 from the co-located data. Because the co-located analysis only deals with changes, the initial amplitudes have been arbitrarily set to zero.
 The co-located ΔSSH projected onto the first EOF indicates a change consistent with the full SSH analysis (Figure 4). This reassures us that the co-located analysis has sufficient spatial resolution. When ΔSH0–1500 results are projected onto the same EOF, the change is about 40% that of the SSH: in comparison, applying the mean slope and intercept to the mean ΔSSH gives a result of 30%.
 In the interval between 1993–1997 and 2004–2008, the mean SSH between 60°S and 60°N increased by 3.4 cm. South of 20°S, the increase was somewhat greater, 4.0 cm. Because of the enhanced rate of increase and much larger area of ocean in the southern hemisphere, the increased ocean volume south of 20°S was 4.8 × 1012 m3,: 47% of the global total volume increase of 1.02 × 1013 m3 over this time period.
 Based on the ΔSH0–1500/ΔSSH correlation analysis and full ΔSSH field, it is estimated that about half of the southern hemisphere volume increase was steric (Figure 3). This was mostly in the upper 1500 m but also included a substantial deep component. South of 40°S, ΔH1500–∞ added more than 50% to ΔSH0–1500 and the mass component was only about 1 cm. Over the 60°S to 20°S domain of our study, the steric increase in volume, based on ΔSSH minus Δass was about 2.5 × 1012 m3.
 Recent estimates of increasing global OHC over this period are about 1.4 × 1023 J in the upper 700 m [Lyman et al., 2010]. Using a representative value of the thermal expansion coefficient of seawater of 10−4°C−1, the estimated increase in 0–700 m global OHC is equivalent to about 3 × 1012 m3 of volume expansion. In other words, the total steric expansion south of 20°S is comparable to the global rate in the upper 700 m.
 Previous authors have found that sparse southern hemisphere sampling leads to large uncertainty in estimated decadal temperature changes [e.g., Gille, 2008]. The present work shows that even the relatively dense sampling of the WOCE-era is not adequate for simple spatial averaging to detect decadal change. Comparison of the full ΔSSH dataset with that at the WOCE-era locations (Figure 1c) shows significant differences. A conclusion is that temperature and steric volume changes at the data co-locations are similarly unrepresentative of the full fields. The importance of global sampling, as done by satellites or extensive in situ arrays such as Argo, is emphasized by these results.
 Finally, it must be reiterated that the correlation analysis performed here identifies components of ΔSSH as either correlated with shallow ΔSH or as spatial mean offsets. These were tentatively identified as deep ΔSH and mass. This is probably not the whole story. Local decadal SH changes may have more than one cause, with uncorrelated abyssal signals possible due to slow overturning and advection [e.g., Purkey and Johnson, 2010]. Similarly, part of the mass change could be correlated with ΔSH0–1500. Many more deep measurements, such as from a deep Argo array, are needed to complete the ocean observing system and close decadal budgets of SSH, SH, and OHC.
 Argo data were collected and made freely available by the International Argo Program and contributing national programs. D. Roemmich participates in Argo through NOAA grant NA17RJ1231. The statements, findings, conclusions, and recommendations herein are those of the authors and do not necessarily reflect the views of NOAA or the Department of Commerce. P. Sutton was supported by New Zealand FRST contract C01X0202.